Underscored: Sure, Sony could halve the price of the PS4. But guess what: They do so already during BF, and the sales are still dropping during that period.
Also, doing that now would be suicide for them. They could do so, but only absolute enthusiasts would then go and buy a PS5, which will be several times more expensive - the exact thing that almost killed the PS3 at launch btw. And that wasn't the only reason why the PS2 kept selling: 3rd world countries got introduced with the PS2 only after the PS3 was released in the west, but the PS4 launched in these countries almost the same time as in the west. Also, many, many bought a PS2 only for Singstar or Buzz - you know, the kind of casuals that later went to the Wii, Kinect and finally smartphones.
bolded: Wrong console, that was the PS3. As a BD-Player the PS4 is way overpriced. I got my BD-3D player in 2013 for about 130€, now they cost half that. A BD-4K player also only costs about 120€, still cheaper than a PS4 even at your purported price tag. No one would buy a PS4 these days just to have a BD-Player.
Additionally, I want to stress that most of the PS2 sales came from the US. But there, Microsoft has now put up much stronger competition than the PS2 had, even with an XBO with middling sales worldwide, as more than half of them come from the US. Playstation has lost part of the US market to the Xbox which was in Sony's hands during the PS2 era.
Long story short, the PS4 doesn't have anything that could give it something near the legs that the PS2 had. PS2 had tons of boosters after the PS3 got revealed, but most of them are not available for the PS4 anymore, so the only reason why the PS4 would sell well into the future would be that Sony royally botches the PS5 launch and makes it too expensive for most people (aka over $599).
Finally, one thing that you can check here is that Playstation plus Xbox each gen results into around 175M. That's true both for PS2/Xbox and PS360, and it looks increasingly like PS4/XBO won't be far off, either.
Just wanted to touch one point.
PS2 also wasn't really the "cheap DVD-player", that myth is easily desbunked looking PS2 had attach ratio about 10 which isn't something very different from the norm at the time.
duduspace11 "Well, since we are estimating costs, Pokemon Red/Blue did cost Nintendo about $50m to make back in 1996"
Mr Puggsly: "Hehe, I said good profit. You said big profit. Frankly, not losing money is what I meant by good. Don't get hung up on semantics"